SOMETIMES IT seems there are a million female jazz vocalists out there and hardly any of them are any good (the male sector is probably even worse, but it's less crowded). Whether it's the piano-prone appeal of Michelle Pfeiffer in The Fabulous Baker Boys or the sulky poses of sundry sensual soubrettes from the past that are to blame, who knows? but there's an apparently endless stream of women who want to snap their fingers and wax lyrical on the age-old verities of the great American songbook while some bloke plays the piano in the background.

Of course, some female vocalists are wonderful, but no one is ever going to beat Billie Holiday at her own game, and the stereotype of the chanteuse delivering smoky ballads with a note of world-weariness in her voice is, after 50 years or more, beginning to grate. So when a new female jazz singer emerges from exactly this tradition, yet who abjures the old finger- snapping and scat-singing approach in favour of attempting to communicate the meaning of a lyric or the subtlety of a musical phrase, you want to roll out the red carpet and bang the gong, big-time. And maybe the best thing about the Swedish vocalist Lisa Ekdahl (who plays the Pizza Express in Soho this month, with the Peter Nordahl Trio) is that she doesn't need to be a jazz singer at all.

In Sweden, Ekdahl is a huge pop star, regularly topping the charts with her own gentle, folk-ish ditties (her debut album went quadruple-platinum); but she has an abiding regard for the distinctive vocal style of trumpeter and singer Chet Baker.

Like Baker, Ekdahl may not have a lot in the way of God-given pipes, but she knows what to do with them. Her debut jazz album, When Did You Leave Heaven? (RCA Victor), isn't perfect, but she can more than carry a tune, and it's usually a tune that has been chosen, with great sensitivity. Her fragile, reassuringly human-sized voice, moves through a selection of standards, accompanied by her regular band.

Though it has only recently come out here, the album was recorded four years ago (in Stockholm, in one day, live, using Fifties equipment). The record wasn't intended for release, as in Sweden it was thought it might affect Ekdahl's pop career. A private pressing of 300 copies were sent out by the record company as gifts to favoured customers, and this resulted in a positive response. So Ekdahl and the group decided to release the album.

When we meet to talk in a Paris cafe, next door to the club where she and the band are playing, Ekdahl, who is 27, talks feelingly about the way she tries to sing jazz, occasionally furrowing her brow as she translates Swedish thoughts into English. "What the band appreciated about me was that I was so relaxed," she says. "I just present the song and I'm patient when they do their solos, which I enjoy. This patience is an important quality because singers often want to take up room all the time, but all of us try to leave a lot of space for each other."

Of Chet Baker, she says: "I'm in love with him all the time since when I was a young teenager. He could do almost anything with his voice because he was musical and it was a good voice, but he had good taste so he didn't do everything he could do. It feels as if he's very confident, and that he trusts the song and the lyrics. He doesn't try to show off. He just sings the song, and it's as if he's resting all the time that he's singing. Can you say that in English?"

Ekdahl's approach to the lyrics of the standard songs is endearingly unfussy. "I don't analyse the lyrics, definitely not - after all, it's not that difficult to understand them - but what I do is try to open up as much as possible. When you sing you are the instrument and you have to use yourself and to open up, and that's what I do, that's my plan. To do that, it's very important that you trust the musicians and that you're comfortable. I also think that by opening up you can communicate on another level. I don't have any idea of what I want to present, and when everything is perfect it's as if you're not doing anything. It's more about surrendering to the tune. Big words for me! When everything's perfect, it's happening faster than thought. You're also responding to others, and that response happens more quickly than you can think, so it's coming from a different place to thought. It's interesting, isn't it?" I start to hum the theme to The Twilight Zone.

Ekdahl is also good on the mythology of vulnerability surrounding female jazz singers. "I feel much more vulnerable when I sing. In life, I feel I have the right to protect myself, but when I sing I have this sense that I'm not allowed this. It's not fair to the music and the art. Yes, it can be uncomfortable, but mostly it's not, because it's an opportunity. You're allowed to do it when you sing, and people expect it of you."

When I press her on what would be an American equivalent to the songs she writes in her pop career (and her albums are like a kind of light folk-rock, with the addition of some world music rhythms), Ekdahl comes up with Leonard Cohen. "It's just a few chords, nothing political, just love and poetry. It's a very Swedish thing, very simple. Nature is a part of it, and big forests."

The governing mood of exquisite melancholy does relate, however, to her jazz singing. "It's like the difference between being depressed and just allowing the sadness to be there," she says of her own songs. "When you listen to Chet Baker you don't have the impression that he's depressed, you just have the impression that he allows the sadness to be there, and it's very nice. It's about opening up and allowing whatever is there to come out."

Seeing Lisa Ekdahl open up in live performance could be a cathartic experience, for us as well as for her.